Diophantine geometry : an introduction / Marc Hindry, Joseph H. Silverman

Auteur principal : Hindry, Marc, 1957-, AuteurCo-auteur : Silverman, Joseph H., 1955-, AuteurType de document : MonographieCollection : Graduate texts in mathematics, 201Langue : anglais.Pays: Allemagne.Éditeur : Berlin : Springer, 2000Description : 1 vol. (XIII- 558 p.) : fig. ; 24 cmISBN: 9780387989815.ISSN: 0072-5285.Bibliographie : Bibliogr. p. [504]-519. Liste des notations. Index.Sujet MSC : 11Gxx, Number theory - Arithmetic algebraic geometry (Diophantine geometry)
11G10, Arithmetic algebraic geometry (Diophantine geometry), Abelian varieties of dimension >1
11J68, Diophantine approximation, transcendental number theory, Approximation to algebraic numbers
11G30, Arithmetic algebraic geometry (Diophantine geometry), Curves of arbitrary genus or genus ≠1 over global fields
14Gxx, Algebraic geometry - Arithmetic problems. Diophantine geometry
En-ligne : Springerlink | Zentralblatt | MathSciNet
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In 1922 Mordell conjectured that every algebraic curve of genus ≥2 has at most finitely many rational points. This conjecture was proved by Faltings in 1983. In 1991 Vojta gave a completely different proof, based on diophantine approximation. Vojta's proof was then simplified by Bombieri. In the textbook under review, the authors work towards Bombieri's proof, giving the reader the necessary background. Unlike several other textbooks in this field, the prerequisites are quite modest, so the book is very useful for instance for a graduate course on diophantine geometry. Each chapter goes along with many exercises. (Zentralblatt)

Bibliogr. p. [504]-519. Liste des notations. Index

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